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Using the prox-regularity notion, we introduce and study a generalized mildly nonconvex variational inequality. We study existence and iterative approximation of its solution under the partially relaxed cocoercivity. Several consequences of the proposed nonconvex variational inequality are also discussed. Journal of Nonlinear Analysis and Application 2 alternative formulation of variational inequalities as multivalued inclusions. Bounkhel et al. , Noor , Pang et al.  has considereddoi:10.5899/2012/jnaa-00146 fatcat:jxv3fmigobal7nmbu4e5pax25u